The number of 4-digit integers in the closed interval [2022, 4482] formed by using the digits 0, 2, 3, 4, 6, 7 is ________.

Question

Smart Achievers · Accepted Answer

(569)

$a$ $b$ $c$ $d$

Case-I:

$a$ = 2, $b$ = 0, $c$ = 2, $d$ can take values 2, 3, 4, 6, 7 $\to$ so 5 numbers

$a$ = 2, $b$ = 0, $c$ can take values 3, 4, 6, 7, d has 6 choices $\to$ so 24 numbers

Case-II:

$a$ = 2, $b$ can take values 2, 3, 4, 6, 7, $c$ and $d$ have 6 choices each $\to$ so 5 × 6 × 6 = 180 numbers

Case-III:

$a$ = 3, $b$ , $c$ , $d$ each has 6 choices $\to$ so 1 × $6^{3}$ = 216 numbers

Case-IV:

$a$ = 4, $b$ = 0, 2, 3, 4, $c$ and $d$ have 6 choices each $\to$ so 4 × $6^{2}$ = 144 numbers

The total number of 4 digit integers

= 5 + 24 + 180 + 216 + 144

= 569

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